FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1147-1175

**Description of metric space as a classification of its finite
subspaces**

Yu. A. Rylov

Abstract

View as HTML
View as gif image
View as LaTeX source

We suggest a new method of metric space description, using its
constituents (finite metric subspaces) as basic objects of
description.
The method allows one to obtain information about the metric
space properties from the metric and to describe the metric
space geometry in terms of its constituents and metric only.
The suggested method permits one to remove the constraints
imposed usually on metric (the triangle axiom and non-negativity
of the squared metric).
Elimination of these constraints leads to a new non-degenerate
geometry.
This geometry is called tubular geometry (T-geometry), because in this
geometry the shortest paths are replaced by hollow tubes.
The T-geometry may be used for description of the space-time
and of other geometries with indefinite metric.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k01/k014/k01411h.htm

Last modified: April 17, 2002